Dynamics of Periodic Waves in a Neural Field Model

Abstract

<jats:p>Periodic travelling waves are observed in various brain activities including visual, motor, language, sleep, and so on. There are several neural field models describing periodic waves assuming nonlocal interaction and, possibly, inhibition, time delay, or some other properties. In this work we study the influence of asymmetric connectivity functions and of time delay on the emergence of periodic waves and on their properties. Nonlinear wave dynamics is studied, including modulated and aperiodic waves. Multiplicity of waves for the same values of parameters is observed. External stimulation in order to restore wave propagation in a damaged tissue is discussed.</jats:p>

Statistical Field Theory and Networks of Spiking Neurons

“…The second term in (21) represents a global limitation to increase the overall number of connections and currents, so that we assume that:…”

“…The potential terms (21) along with its corrections (262) evaluated at the background field Ψ 0 yield a constant U (Ψ 0 ). This constitutes a modification to the scale α which is replaced by α + U ′′ (Ψ 0 ).…”

“…Neural fields theory, because it is a mean field approach that focuses on large scale effects, has a large range of applications, and has been extended along various lines. This approach allows for travelling wave solutions, possibly periodic (see [20] [21] and references therein). Stochastic effects in firing rates or other relevant variables have been introduced [10] [11][12] [13] [14] to model perturbations and diffusion patterns in the pulse waves dynamics.…”